If the slope of line l is x, and the slope of line m is x+2, and l⊥ m, what is x?

Mathematics

1 answer:

salantis [7]2 years ago

6 0

Answer:

The answer to your question is: x = -1

Step-by-step explanation:

Data

slope of l = x

slope of m = x +2

they are ⊥

Process

If they are ⊥, then, x + 2 = - 1/x

x(x + 2) = -1

x² + 2x = -1

x² + 2x + 1 = 0

(x + 1)² = 0

x + 1 = 0

x = -1

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What is the quotient: (6x4 + 15x3 + 10x2 + 10x + 4) ÷ (3x2 + 2)?

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Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

$\frac{\left(6x^4+15x^3+10x^2+10x+4\right)}{\left(3x^2+2\right)}$

Now, we will find the quotient by factoring the numerator:

$\mathrm{Use\:the\:rational\:root\:theorem}\\a_0=4,\:\quad a_n=6\\\\\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:4,\:\quad \\\mathrm{The\:dividers\:of\:}a_n:\quad 1,\:2,\:3,\:6\\\\\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:4}{1,\:2,\:3,\:6}\\\\-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2\\\\=\left(x+2\right)\frac{6x^4+15x^3+10x^2+10x+4}{x+2}\\\\=\frac{6x^4+15x^3+10x^2+10x+4}{x+2}=6x^3+3x^2+4x+2\\\\$

Now, we will factor it again:

$=\left(6x^3+3x^2\right)+\left(4x+2\right)\\\\=2\left(2x+1\right)+3x^2\left(2x+1\right)\\\\=\left(2x+1\right)\left(3x^2+2\right)$

At last we get our factorised form :

$=\left(x+2\right)\left(2x+1\right)\left(3x^2+2\right)\\\\=\frac{\left(x+2\right)\left(2x+1\right)\left(3x^2+2\right)}{3x^2+2}\\\\=\left(x+2\right)\left(2x+1\right)\\\\=2x^2+5x+2$